Explanation Given: ∫ 9 ∞ d x x 12 / 5 Calculation: The given integral is improper as the interval of integration is [ 9 , ∞ ) which is not closed. If an end point of the interval is infinity, we make use of the limit and so evaluate: ∫ 9 ∞ d x x 12 / 5 = lim M → ∞ ∫ 9 M d x x 12 / 5 ∫ 9 ∞ d x x 12 / 5 = lim M → ∞ ∫ 9 M d x x 12 / 5 = lim M → ∞ [ x − 12 5 + 1 − 12 5 + 1 ] 9 M = lim M → ∞ [ x − 7 / 5 − 7 5 ] 9

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8, Problem 78CRE

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If the following improper integral converges and if so, evaluate it.

$\begin{array}{l} \int_{9}^{\infty} \frac{d x}{x^{12 / 5}} \end{array}$

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Chapter 8, Problem 77CRE

Chapter 8, Problem 79CRE

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Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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If the following improper integral converges and if so, evaluate it. ∫ 9 ∞ d x x 12 / 5

Solution Summary: The author analyzes how the given improper integral converges. If an end point of the interval is infinity, we use the limit.

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If the following improper integral converges and if so, evaluate it.

$\begin{array}{l} \int_{9}^{\infty} \frac{d x}{x^{12 / 5}} \end{array}$

Want to see the full answer?

Chapter 8 Solutions

If the following improper integral converges and if so, evaluate it. ∫ 9 ∞ d x x 12 / 5

Solution Summary: The author analyzes how the given improper integral converges. If an end point of the interval is infinity, we use the limit.

Concept explainers

Videos

If the following improper integral converges and if so, evaluate it. ∫9∞dxx12/5

Want to see the full answer?

Chapter 8 Solutions

If the following improper integral converges and if so, evaluate it.

$\begin{array}{l} \int_{9}^{\infty} \frac{d x}{x^{12 / 5}} \end{array}$